Solve This: Leave Me a Lawn!

July 27, 2015
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Nobody really got the answer quite right in my opinion, but we have to give the award to "StraightSh00ter357" for shear perseverance. But here's what Wanda really said:

"Guys, with George's assumptions that all blades of the grass are gone over just once, the answer is easy. You all have the same size, same speed mower so you all mow the same amount of area per unit time. And since you all have the same size lawns then no matter what pattern (again under George's assumptions) you all take the same amount of time to mow your lawn. There is no optimum!  Uh... more coffee gentlemen?"

--Paul Mauldin

Original Puzzle:

George, Tom and Phil – three of Hinterland Electric’s long time engineers are having coffee in the company cafeteria and discussing their common dislike of yardwork. The three men live in the same neighborhood, have identical front lawns and even the same brand and model of self-propelled lawn mowers.

“I got an idea,” said George who also has a degree in math and loves analysis, “why don’t we figure out an optimal lawn mowing pattern that will minimize the time spent cutting the grass? I already know, but let’s see if you guys can figure it out.”

He continued: “Assume that the mower runs at constant speed. Our lawns are all the same – 30’X40’. Assume no grass is gone over more than once with the blade turning and the engine is shut off when the last grass blade is cut. Time starts when the first blades of grass are cut and ends when the lawn is completely mowed.”

“Well, I don’t need to do much figuring,” snorted Phil, the communication expert, “I thought about this years ago and determined that the simplest pattern is the best.”

Phil quickly sketched out his pattern on a napkin.

“No, no, no!,” chastened George as he grabbed a napkin, “A diagonal pattern is optimal. Of course the slant depends on the aspect ratio which is the ratio of length to width of the lawn. I’d have to get my calculator to figure out the exact details but it’s similar to this.”

Tom (a software engineer with an artistic bent) just smiled and drew a spiral pattern on his napkin. “This is a little more complex but it will take the least amount of time and leave a beautiful pattern in the grass as well. The trick is to gradually move from a spiral pattern to a rectangle as you get closer to the edges – like this.”

Meanwhile – Wanda, the cafeteria server, came over to clear the table before going home (since their boss was out of town attending the annual week-long budget meeting in Las Vegas, the engineers had spent most of the afternoon over coffee and discussion). Noticing her curiosity over the drawings they explained the problem, including the dimensions of the lawns and other assumptions. Then (smiling to themselves) they invited her to give it a try.

To their utter surprise she immediately responded with an answer and explained why it was correct!

- - -

Wanda laughed all the way home.

Until severe Winter weather hit, George, Tom and Phil began taking their coffee breaks two blocks away at Kathy’s Kaffeen Korner.

What might Wanda’s answer have been?

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